Bayesian parameter estimation for dynamical models in systems biology
Fig 7
Parameter estimation results for the MAPK model in the limit cycle regime with varied sampling strategies.
(A) The equidistant sampling data includes 30 samples taken every 2 minutes over 0 < t ≤ 60 (min). The non-equidistant sampling data includes 20 total samples with two sampling rates; there are 5 samples taken every 5 minute for the first 30 minutes and 15 samples taken every 2 minutes for 30 additional minutes. The oscillations only data set only includes samples from the oscillations with 15 samples taken every two minutes over the interval t ∈ (30, 60]. (B) The fraction of the 30,000 simulations that yield limit cycle or fixed point trajectories, with parameter samples from the prior, and the posterior distribution associated with each data set. (C–E) Marginal posterior distributions of the model parameters. Distributions are visualized by fitting a kernel density estimator to 2,524,800 samples for the equidistant sampling data, 763,080 for the non-equidistant sampling data, and 1,305,720 for the oscillations only data. (F–H) Two-dimensional scatter plots reveal relationships between k4 and α that are necessary to produce limit oscillations. Simulations with blue points produce limit cycle oscillations, and those with red points produce fixed points. Darker regions indicate a higher probability of observing the corresponding parameter values.